Good points. Perhaps moral bonus would be more appropriate. People take pride when one of their own is competing - especially if they do well.
Directly to your points:
Why would the innkeeper make more gold while his Lord is away?
Because people are spending their evenings at said inn discussing the valiant noble and whatever news they hear from the tournament. If one of their own were not there, they would be less interested in spending time and money in relation to a tourney. As above though, perhaps a morale bonus might be better.
Why would the mines produce more gold?
Because the people are proud and feel a sense of unity and thus work harder with less fuss. They start working for the good of the cause instead of just because they have to. Again, moral bonus might be better than productivity.
Also, it would hard to determine what "his region" means. Does it only apply to Lords?
I intended it to mean the lord of the region and/or any noble with an estate in that region. I would not expect a flat stacking bonus as this could be too much but I would think that multiple nobles participating from the same region would result in a slightly higher bonus than just one.
Do you hand out benefits pro rate of the size of the estate?
Not a bad idea but then you have to consider that a lord may not have an estate. I would keep it simple and have a flat bonus for one participant with tiny increases for additional participants beyond the first.
What about landless nobles?
They do not spur a bonus as no one considers them their own and is there to cheer them on and plain feel good about their Lord/Knight being off in the tournament. A benefit of having peasants of your own!
Maybe it would be best to apply a bonus to the unit instead of to the region. Something like an equipment upgrade if you do well for example?
I think that a moral bonus to your troops would be in order or the like!
